%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ027-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:23:08 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 149 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 147 ( 55 ~; 92 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_there_is_an_answer,axiom,
! [VAR_0] : ~ answer(VAR_0),
file('theBenchmark.p',prove_there_is_an_answer) ).
cnf(c_1,plain,
~ answer(A),
inference(clausify,[status(thm)],[prove_there_is_an_answer]) ).
fof(a_liar_b_normal,axiom,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
file('theBenchmark.p',a_liar_b_normal) ).
cnf(c_3,plain,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
inference(clausify,[status(thm)],[a_liar_b_normal]) ).
fof(a_liar_b_truthteller,axiom,
( answer(a_liar_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(liar(a)) ),
file('theBenchmark.p',a_liar_b_truthteller) ).
cnf(c_4,plain,
( answer(a_liar_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(liar(a)) ),
inference(clausify,[status(thm)],[a_liar_b_truthteller]) ).
fof(a_and_b_normal,axiom,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
file('theBenchmark.p',a_and_b_normal) ).
cnf(c_6,plain,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(clausify,[status(thm)],[a_and_b_normal]) ).
fof(a_normal_b_truthteller,axiom,
( answer(a_normal_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(normal(a)) ),
file('theBenchmark.p',a_normal_b_truthteller) ).
cnf(c_7,plain,
( answer(a_normal_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(normal(a)) ),
inference(clausify,[status(thm)],[a_normal_b_truthteller]) ).
cnf(c_14,plain,
( ~ a_truth(truthteller(b))
| ~ a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_15,plain,
( ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_17,plain,
( ~ a_truth(truthteller(b))
| ~ a_truth(liar(a)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_18,plain,
( ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(b_says_a_not_lower_than_b,axiom,
a_truth(says(b,not_lower(a,b))),
file('theBenchmark.p',b_says_a_not_lower_than_b) ).
cnf(c_20,plain,
a_truth(says(b,not_lower(a,b))),
inference(clausify,[status(thm)],[b_says_a_not_lower_than_b]) ).
fof(a_says_a_lower_than_b,axiom,
a_truth(says(a,lower(a,b))),
file('theBenchmark.p',a_says_a_lower_than_b) ).
cnf(c_21,plain,
a_truth(says(a,lower(a,b))),
inference(clausify,[status(thm)],[a_says_a_lower_than_b]) ).
fof(no_one_lower_than_liars,axiom,
! [VAR_0,VAR_1] :
( ~ a_truth(liar(VAR_1))
| ~ a_truth(lower(VAR_0,VAR_1)) ),
file('theBenchmark.p',no_one_lower_than_liars) ).
cnf(c_25,plain,
( ~ a_truth(liar(B))
| ~ a_truth(lower(A,B)) ),
inference(clausify,[status(thm)],[no_one_lower_than_liars]) ).
fof(liars_lower_than_normal,axiom,
! [VAR_0,VAR_1] :
( a_truth(liar(VAR_0))
| ~ a_truth(normal(VAR_1))
| ~ a_truth(lower(VAR_0,VAR_1)) ),
file('theBenchmark.p',liars_lower_than_normal) ).
cnf(c_26,plain,
( a_truth(liar(A))
| ~ a_truth(normal(B))
| ~ a_truth(lower(A,B)) ),
inference(clausify,[status(thm)],[liars_lower_than_normal]) ).
fof(normal_and_liars_lower_than_truthtellers,axiom,
! [VAR_0,VAR_1] :
( a_truth(liar(VAR_0))
| a_truth(normal(VAR_0))
| ~ a_truth(truthteller(VAR_1))
| ~ a_truth(lower(VAR_0,VAR_1)) ),
file('theBenchmark.p',normal_and_liars_lower_than_truthtellers) ).
cnf(c_27,plain,
( a_truth(liar(A))
| a_truth(normal(A))
| ~ a_truth(truthteller(B))
| ~ a_truth(lower(A,B)) ),
inference(clausify,[status(thm)],[normal_and_liars_lower_than_truthtellers]) ).
fof(not_lower_or_lower,axiom,
! [VAR_0,VAR_1] :
( a_truth(lower(VAR_0,VAR_1))
| a_truth(not_lower(VAR_0,VAR_1)) ),
file('theBenchmark.p',not_lower_or_lower) ).
cnf(c_31,plain,
( a_truth(lower(A,B))
| a_truth(not_lower(A,B)) ),
inference(clausify,[status(thm)],[not_lower_or_lower]) ).
fof(liars_and_normal_lie,axiom,
! [VAR_0,VAR_1] :
( a_truth(normal(VAR_1))
| a_truth(liar(VAR_1))
| ~ a_truth(says(VAR_1,VAR_0))
| a_truth(VAR_0) ),
file('theBenchmark.p',liars_and_normal_lie) ).
cnf(c_34,plain,
( a_truth(normal(B))
| a_truth(liar(B))
| ~ a_truth(says(B,A))
| a_truth(A) ),
inference(clausify,[status(thm)],[liars_and_normal_lie]) ).
fof(truthtellers_and_normal_tell_truth,axiom,
! [VAR_0,VAR_1] :
( a_truth(normal(VAR_1))
| a_truth(truthteller(VAR_1))
| ~ a_truth(says(VAR_1,VAR_0))
| ~ a_truth(VAR_0) ),
file('theBenchmark.p',truthtellers_and_normal_tell_truth) ).
cnf(c_35,plain,
( a_truth(normal(B))
| a_truth(truthteller(B))
| ~ a_truth(says(B,A))
| ~ a_truth(A) ),
inference(clausify,[status(thm)],[truthtellers_and_normal_tell_truth]) ).
fof(person_is_one_type,axiom,
! [VAR_0] :
( a_truth(normal(VAR_0))
| a_truth(liar(VAR_0))
| a_truth(truthteller(VAR_0)) ),
file('theBenchmark.p',person_is_one_type) ).
cnf(c_41,plain,
( a_truth(normal(A))
| a_truth(liar(A))
| a_truth(truthteller(A)) ),
inference(clausify,[status(thm)],[person_is_one_type]) ).
cnf(c_49,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(lower(a,b)) ),
inference(resolve,[status(thm)],[c_34,c_21]) ).
cnf(c_109,plain,
( a_truth(lower(B,C))
| a_truth(normal(A))
| a_truth(truthteller(A))
| ~ a_truth(says(A,not_lower(B,C))) ),
inference(resolve,[status(thm)],[c_35,c_31]) ).
cnf(c_53,plain,
( a_truth(lower(a,b))
| a_truth(normal(b))
| a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_109,c_20]) ).
cnf(c_110,plain,
( a_truth(liar(a))
| a_truth(normal(a))
| ~ a_truth(truthteller(b))
| a_truth(normal(a))
| a_truth(liar(a)) ),
inference(resolve,[status(thm)],[c_49,c_27]) ).
cnf(c_111,plain,
( a_truth(liar(a))
| ~ a_truth(truthteller(b))
| a_truth(normal(a))
| a_truth(liar(a)) ),
inference(copy,[status(thm)],[c_110]) ).
cnf(c_67,plain,
( ~ a_truth(truthteller(b))
| a_truth(normal(a))
| a_truth(liar(a)) ),
inference(copy,[status(thm)],[c_111]) ).
cnf(c_112,plain,
( a_truth(liar(a))
| ~ a_truth(normal(b))
| a_truth(normal(a))
| a_truth(liar(a)) ),
inference(resolve,[status(thm)],[c_49,c_26]) ).
cnf(c_68,plain,
( ~ a_truth(normal(b))
| a_truth(normal(a))
| a_truth(liar(a)) ),
inference(copy,[status(thm)],[c_112]) ).
cnf(c_113,plain,
( a_truth(normal(b))
| a_truth(truthteller(b))
| ~ a_truth(liar(b)) ),
inference(resolve,[status(thm)],[c_25,c_53]) ).
cnf(c_114,plain,
( a_truth(normal(b))
| a_truth(truthteller(b))
| a_truth(normal(b))
| a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_113,c_41]) ).
cnf(c_115,plain,
( a_truth(normal(b))
| a_truth(normal(b))
| a_truth(truthteller(b)) ),
inference(copy,[status(thm)],[c_114]) ).
cnf(c_77,plain,
( a_truth(normal(b))
| a_truth(truthteller(b)) ),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_78,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(normal(b)) ),
inference(resolve,[status(thm)],[c_77,c_67]) ).
cnf(c_82,plain,
( ~ a_truth(normal(a))
| a_truth(normal(b)) ),
inference(resolve,[status(thm)],[c_77,c_14]) ).
cnf(c_116,plain,
( a_truth(normal(a))
| a_truth(normal(b))
| ~ a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_17,c_78]) ).
cnf(c_117,plain,
( a_truth(normal(b))
| a_truth(normal(a))
| a_truth(normal(b)) ),
inference(resolve,[status(thm)],[c_116,c_77]) ).
cnf(c_96,plain,
( a_truth(normal(a))
| a_truth(normal(b)) ),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_118,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_96,c_68]) ).
cnf(c_97,plain,
( a_truth(liar(a))
| a_truth(normal(a)) ),
inference(copy,[status(thm)],[c_118]) ).
cnf(c_119,plain,
( a_truth(normal(a))
| ~ a_truth(normal(b)) ),
inference(resolve,[status(thm)],[c_18,c_97]) ).
cnf(c_120,plain,
( a_truth(normal(a))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_119,c_96]) ).
cnf(c_105,plain,
a_truth(normal(a)),
inference(copy,[status(thm)],[c_120]) ).
cnf(c_106,plain,
a_truth(normal(b)),
inference(resolve,[status(thm)],[c_105,c_82]) ).
cnf(c_121,plain,
~ a_truth(normal(b)),
inference(resolve,[status(thm)],[c_105,c_15]) ).
cnf(c_108,plain,
$false,
inference(resolve,[status(thm)],[c_106,c_121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ027-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:08:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3183016 was started by sandbox2 on n015,
% 0.09/0.37 % Sat Sep 26 05:08:13 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 30.
% 0.09/0.38 % Level of proof is 8.
% 0.09/0.38 % Maximum clause weight is 23.000.
% 0.09/0.38 % Given clauses 68.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------